In the pharmaceutical industry, stability testing is conducted as part of product development to test the quality of pharmaceutical formulations. Stability of a pharmaceutical product can be defined as the capability of a particular formulation in a specific container/closure system to remain within its physical, chemical, and/or microbiological specifications. In particular, stability of a pharmaceutical product determines the extent to which the product retains the expected properties from packaging and throughout its period of storage and use. Stability testing thus evaluates, often repeatedly over time, the effect of the formulation and environmental factors on the quality of the product, thereby predicting its shelf life. Other industrial sectors also use stability testing, such as the food, beverage and cosmetics industries, to evaluate product robustness over time.
Traditionally, when performing stability testing, all possible combinations of factors involved need to be tested, which necessitates a large number of experimental trials that can be costly and time-consuming. Using the biopharmaceutical industry as an example, a user can complete a stability study by testing all combinations of various factors involved in a formulation, including buffers (4 levels), pH (4 levels), preservatives (3 levels) and concentration of active pharmaceutical ingredient (API) (3 levels), thus yielding 144 trial formulations (4*4*3*3). In addition, the trials can be conducted at multiple points in time, such as at 0, 1, 3, 6, 9, 12, 18, 24 and 36 months and with two or three different analytical methods. The cost of testing each trial formulation can be from $1,000 to $5,000 USD. Therefore, the overall testing expense can be quite high, especially if all 144 trial formulations are tested at each time point with several different analytical methods.
Product characteristic testing is used in various industries, not limited to the biopharmaceutical industry. Moreover, testing can be conducted in relation to various product characteristics, including characteristics associated with the product itself, a process for developing the product, or a procedure related to the product. In general, an experimental design for testing a product characteristic can be created based on (i) one or more factors, each factor specifies a parameter for testing the product characteristic, (ii) one or more levels for each factor, where each level specifies a different setting (e.g., value) for the corresponding factor and (iii) one or more partitions (e.g., points in time) at which the testing needs to be conducted.
As an example, in the field of mass spectrometry (MS), a scientist needs to routinely optimize and adjust a MS system to deliver strong and stable signals for selected peaks and low signals for interfering peaks. Such an MS system has multiple factors, each can be adjusted at 6 to 10 different levels. At minimum, assuming there are 4 factors and each factor has 6 levels, the number of combinations to investigate per time point is 1296 (6^4). As another example, in the field of market research, responses of people in five age groups can be evaluated with respect to a variety of factors related to product advertisement, including product packaging (fancy, standard, or environmental), pricing ($10, $12, or $14 USD), and branding (generic or sophisticated). Hence, 90 trials need to be conducted to investigate all combinations of the different levels of the various factors involved. In many cases, it may not be feasible to perform all 90 trials. Therefore, 30 trials may be conducted to study the main features and their potential synergies (e.g., interactions). However, because the cost involved with conducting the 30 trials per time point is still high, there is a desire to reduce the number of trials even further while capturing the main features.
Traditional methods for reducing the number of experiments used to test a product characteristic usually only work with systems involving factors having 2 different levels. Hence, there exists a market demand for algorithms that can efficiently handle problems involving multilevel factors (i.e. factors with more than 2 levels). There are several challenges to creating such an algorithm. For example, experimental designs that provide optimal statistical conditions for a series of trials in an investigation are often of the orthogonal array type. While orthogonal arrays are relatively straightforward to apply, they can only be used in very limited cases for certain sets of factors and certain number of trial runs due to their mathematical properties. It cannot be guaranteed that for a given set of factors, levels and runs an orthogonal array can be defined and used for the purpose of creating a test plan.